In practice, however, we need to truncate the expansion at some finite order and have to take into account the systematic error due to the truncation.
We thus studied the issue of the truncation error of the hopping parameter expansion, focusing on the determination of the critical point \(\kappa _c\)  in heavy quark QCD.
In the case of worst convergence, we found that, the truncation error on \(N_t=4\)  lattices is well under control up to around \(\kappa \sim 0.1\) , ensuring the previous next-to-leading order calculations of \(\kappa _c\)  for \(N_t=4\)  [1]}, [2]}.
We also found that the truncation error increases as \(N_t\)  increases, such that, already for \(N_t=6\) , significant effect from higher-order terms exist around \(\kappa _c\)  determined by a next-to-leading order calculation.
